Questions tagged [sequence-of-function]

Use this tag only when your query is about sequences of functions. Don't use this tag for any other sequence such as sequences of real numbers or sequences of complex numbers etc.

248 questions
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prove that if a series of functions converges uniformly in D… [closed]

I met this question searching online for exercises but I can't seem to solve it. Prove that if the series of functions $\sum_{n=1}^\infty f_n(x)$ converges uniformly in group D, then the sequence of ...
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Equicontinuity with respect to a sequence of points? (terminology question)

I'm searching for an established term for "equicontinuity with respect to a sequence of points" for a function. Let $\{f_k\}$ be a family of functions and $\{x_k\}$ some associated points. My version ...
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Understanding technique for proving uniform convergence of sequence of functions

Consider the sequence of functions $f_n(x)=\frac{x}{nx+1}, x\in(0,1).$ Does it converge uniformly? If $f_n$ are differentiable $\forall n$ and $f_n(x)$ converges pointwise to $f(x)$, this technique ...
Consider the sequence of functions $f_k :A \rightarrow \mathbb{R}$. Suppose that $\{f_k\} \rightarrow f$ uniformly in A and $f_k$ is continuous in A $\forall k$. Prove that if $x_0 \in A$ and \$\{x_k \...